Problem: The following line passes through point $(3, 8)$ : $y = \dfrac{3}{2} x + b$ What is the value of the $y$ -intercept $b$ ?
Explanation: Substituting $(3, 8)$ into the equation gives: $8 = \dfrac{3}{2} \cdot 3 + b$ $8 = \dfrac{9}{2} + b$ $b = 8 - \dfrac{9}{2}$ $b = \dfrac{7}{2}$ Plugging in $\dfrac{7}{2}$ for $b$, we get $y = \dfrac{3}{2} x + \dfrac{7}{2}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(3, 8)$